On the solution of Lambert's problem by regularization

Torre, David De la; Flores, Roberto; Fantino, Elena

doi:10.1016/j.actaastro.2018.10.010

Cited by 18 publications

(9 citation statements)

References 35 publications

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“…Once a TOF is determined, the intercept orbit can be ascertained by solving equation (23), in which equation (7) is an equal constraint used to determine the terminal positon vector r 2 . Then, substituting the value of P into equation (15), the initial velocity vector v 1 of the EKV can be calculated by Lagrangian coefficients as follows:…”

Section: 2mentioning

confidence: 99%

“…Substituting equation (15) into equation (22), the semimajor axis of the intercept orbit is rewritten as follows:…”

Section: Partialmentioning

confidence: 99%

“…Substituting equations (15) and (49) into equation (39) and partially differentiating g 2 with respect to P yields…”

Section: Partialmentioning

confidence: 99%

“…An iterative method based on Householder's root solver was designed in [14], where the first and second derivatives of the time-of-flight (TOF) equation are analytically derived to increase the rate of convergence. In [15], Levi-Civita regularization was applied to Lambert's problem, and a Newton-Raphson method in combination with safety checks was adopted to achieve both speed and robustness. These works have successfully promoted the application of Lambert's problem in the space science community.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Midcourse Guidance Algorithm for Exoatmospheric Interception Using Analytical Gradients

Chen

Yang

et al. 2019

International Journal of Aerospace Engineering

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This paper is aimed at providing a semianalytical method to solve the optimal exoatmospheric interception problem with the minimum fuel consumption. A nonlinear programming (NLP) problem with the minimum velocity increment, which involves Lambert’s problem with unspecified time-of-flight, is firstly formulated. Then, a set of Karush-Kuhn-Tucker conditions and the Jacobian matrix corresponding to those conditions are derived in an analytical manner, even though the derivatives are mathematically complicated and computationally onerous. Therefore, the Newton-Raphson method can be used to efficiently solve this problem. To further decrease computational cost, a near-optimal initialization method reducing the dimension of the search space is presented to provide a better initial guess. The performance of the proposed method is assessed by numerical experiments and comparison with other methods. The results show that this method is not only of high computational efficiency and accuracy but also applicable to onboard guidance.

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Section: 2mentioning

confidence: 99%

“…Substituting equation (15) into equation (22), the semimajor axis of the intercept orbit is rewritten as follows:…”

Section: Partialmentioning

confidence: 99%

“…Substituting equations (15) and (49) into equation (39) and partially differentiating g 2 with respect to P yields…”

Section: Partialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Midcourse Guidance Algorithm for Exoatmospheric Interception Using Analytical Gradients

Chen

Yang

et al. 2019

International Journal of Aerospace Engineering

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“…The error of the solution depends on the accuracy of the initial approximation of the perturbation function. General principles of the development of perturbation theory in coordinates were analyzed in operations [6][7][8] studied the use of regularizing variables for calculation of trajectories of motion. in operation.…”

Section: Introductionmentioning

confidence: 99%

About the decision regularized equations of perturbed motion body

Petelina

2019

E3S Web Conf.

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The article deals with determination of the second- and higher-order perturbations in Cartesian coordinates and body motion velocity constituents. A special perturbed motion differential equations system is constructed. The right-hand sides of this system are finite polynomials relative to an independent regularizing variable. This allows constructing a single algorithm to determine the second and higher order perturbations in the form of finite polynomials relative to some regularizing variables that are chosen at each approximation step. Following the calculations results with the use of the developed method, the coefficients of approximating polynomials representing rectangular coordinates and components of the regularized body speed were obtained. Comparison with the results of numerical integration of the equations of disturbed motion shows close agreement of the results. The developed methods make it possible to calculate, by the approximating polynomials, any intermediate point of the motion trajectory of the body.

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On the solution to every Lambert problem

Russell

2019

Celest Mech Dyn Astr

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On the solution of Lambert's problem by regularization

Abstract: Portal del coneixement obert de la UPC http://upcommons.upc.edu/e-prints Aquesta és una còpia de la versió author's final draft d'un article publicat a la revista Acta astronautica.

Cited by 18 publications

References 35 publications

Optimal Midcourse Guidance Algorithm for Exoatmospheric Interception Using Analytical Gradients

Optimal Midcourse Guidance Algorithm for Exoatmospheric Interception Using Analytical Gradients

About the decision regularized equations of perturbed motion body

On the solution to every Lambert problem

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